Abstract
We investigate a quasi-static quantum Stirling cycle employing a spin-chain-star working fluid, comprising a central ancilla coupled to multiple Heisenberg chains via anisotropic exchange. A unitary transformation reduces the many-body thermodynamics to exact diagonalisation within a Hilbert space of dimension two to the power of the chain number plus one. We evaluate purely transverse, isotropic in-plane, and fully anisotropic configurations. The cycle exhibits tunable heat engine, refrigerator, and quantum accelerator regimes governed by ancilla frequency and coupling strength disparities. The transverse configuration demonstrates superior engine performance approaching the Carnot limit, corroborated by a closed-form partition function that permits the engine-refrigerator boundary to be evaluated exactly at arbitrary chain number. Conversely, the fully anisotropic architecture undergoes a genuine many-body crossover from engine to refrigerator with escalating chain multiplicity, driven by collective coupling amplification. Regenerator functionality proves non-ideal, rendering the cycle irreversible. Perfect regeneration emerges only along a precise quantum resonance locus where isochoric heat exchanges balance. Deviating from this condition exacerbates thermal imbalance with increasing system size, constituting the primary irreversibility source. Finally, kinematic coherence maximizes during cold-bath compression and amplifies with anisotropy and chain number. Originating from Hamiltonian basis rotation rather than non-equilibrium dynamics, this coherence remains dissociated from thermodynamic efficacy.